Find cot 0 if cos 0=3/13
3/4 root 10
you make a right triangle. use Pythagorean theorem. and find the opposite side. then reduce the radical of 160. and do tan and then flip them around to make cot.
The value of:
\(\cot \theta=\dfrac{3}{4\sqrt{10}}\)
We are given,
\(\cos \theta=\dfrac{3}{13}\)
We know that cos θ is the ratio of base and hypotenuse of a right angled triangle corresponding to θ.
On applying Pythagorean Theorem in ΔABC we get:
\(13^2=3^2+a^2\\\\\\i.e.\\\\\\169=9+a^2\\\\\\a^2=160\\\\\\i.e.\\\\\\a=4\sqrt{10}\)
Hence, the value of \(\cot \theta\) is defined as the ratio of base to perpendicular length of the triangle.
Hence,
\(\cot \theta=\dfrac{3}{4\sqrt{10}}\)